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An integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners

Ismail, Munira and Mohd. Murid, Ali Hassan and Sanugi, Bahrom (2006) An integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners. International Journal on Simulation and Process Modelling, 2 (1/2). pp. 25-32. ISSN 1740-2123

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Abstract

In this paper we introduce a new integral equation for computing the numerical solution of the Riemann problem in a simply connected region bounded by curves having a finite number of corners in the complex plane. The solution to this problem may be characterised as the solution to a singular integral equation on the boundary. By using results of Hille and Muskhelishvili, the theory is extended to include boundaries with corners which are rarely used for numerical computation. Following Swarztrauber's derivation of an integral equation for the numerical solution of Dirichlet problem in a region of general shape, we use the Picard iteration method to obtain an iterative formula which removes singularities during numerical integration. The result is a direct method which does not involve conformal mapping. The numerical examples given demonstrate the effectiveness of this new strategy

Item Type:Article
Uncontrolled Keywords:integral equation; riemann problem; dirichlet problem; boundary with corners; picard iteration method; boundary value problems; analytic functions
Subjects:Q Science > Q Science (General)
Divisions:Science
ID Code:8182
Deposited By: Ms Zalinda Shuratman
Deposited On:02 Apr 2009 06:17
Last Modified:14 Oct 2010 01:53

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